Given NLM = 50^, so QLM = 50^.

The line PLQ is a straight line.
The line LM bisects $\angle QLN$, which means $\angle QLM = \angle MLN$.
Given $\angle NLM = 50^\circ$, so $\angle QLM = 50^\circ$.
Therefore, $\angle QLN = \angle QLM + \angle MLN = 50^\circ + 50^\circ = 100^\circ$.
Angles on a straight line add up to $180^\circ$. So, $\angle PLN + \angle QLN = 180^\circ$.
Given $\angle PLN = x^\circ$.

$$x^\circ + 100^\circ = 180^\circ$$ $$x = 180 - 100$$ $$x = 80$$

The value of $x$ is $\boxed{80}$.

We are given that line LM is parallel to line NR (LM || NR).
Consider the transversal line LN.
Since LM || NR, the alternate interior angles are equal.
Therefore, $\angle LNR = \angle MLN$.
We know $\angle MLN = 50^\circ$.
So, $\angle LNR = 50^\circ$.

Now, consider the angles around point N.
The angle $\angle RNS$ is given as $y^\circ$.
The angle $\angle LNS$ is formed by the ray NL and the ray NS.
From the diagram, $\angle LNS$ is the sum of $\angle LNR$ and $\angle RNS$.
$\angle LNS = \angle LNR + \angle RNS = 50^\circ + y^\circ$.

Consider the transversal line PS.
Since LM || NR, the corresponding angles are equal.
The angle $\angle PLN = x^\circ = 80^\circ$.
The angle corresponding to $\angle PLN$ is $\angle LNS$.
Therefore, $\angle LNS = \angle PLN$.

$$50^\circ + y^\circ = 80^\circ$$ $$y = 80 - 50$$ $$y = 30$$

The value of $y$ is $\boxed{30}$.